{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 03\n",
    "\n",
    "# 正多边形\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e85c3d7-148d-4b79-9a7e-b0bb6c7c5609",
   "metadata": {},
   "source": [
    "该代码使用`matplotlib`库绘制了一系列不同边数的正多边形，每个多边形的边数从$3$（三角形）到$8$（八边形），并逐个展示每个图形。正多边形是指边长相等、内角相等的多边形，其中三角形、正方形、五边形等都是正多边形的实例。\n",
    "\n",
    "### 代码细节\n",
    "\n",
    "1. **多边形构造**：\n",
    "   - 使用`RegularPolygon`生成中心位于原点$(0, 0)$、半径为$1$的正多边形。半径指的是从中心到任一顶点的距离，控制了多边形的大小。\n",
    "   - 在每次循环中，`num_vertices`的值决定了多边形的边数，从而生成不同的正多边形形状。\n",
    "\n",
    "2. **可视化**：\n",
    "   - 每个多边形都使用透明度$0.2$并绘制黑色边框，使图形具有柔和的效果。\n",
    "   - 设置绘图区域范围$(-1.5, 1.5)$，确保所有顶点都在可视区域内。\n",
    "\n",
    "### 多边形几何特性\n",
    "\n",
    "对于每个多边形，内角和公式为：\n",
    "\n",
    "$$\n",
    "\\text{内角和} = (n - 2) \\times 180^\\circ\n",
    "$$\n",
    "\n",
    "其中$n$是多边形的边数。此外，正多边形的每个内角大小为：\n",
    "\n",
    "$$\n",
    "\\text{内角} = \\frac{(n - 2) \\times 180^\\circ}{n}\n",
    "$$\n",
    "\n",
    "### 总结\n",
    "\n",
    "该代码通过可视化展示了从三角形到八边形的正多边形变化，并直观体现了随着边数增加，正多边形逐渐接近圆的外观特性。这种逐步变化展示了正多边形在几何上的对称性与一致性。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "123562a4-baa4-4e99-aa15-a92a1176b89c",
   "metadata": {},
   "source": [
    "## 绘制不同边数的正多边形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a1919c0c-ec2f-44b9-8b9b-17aac430e5e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import RegularPolygon\n",
    "import numpy as np\n",
    "\n",
    "for num_vertices in [3, 4, 5, 6, 7, 8]:  # 循环不同边数的多边形\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_aspect('equal')\n",
    "\n",
    "    hexagon_inner = RegularPolygon((0, 0), numVertices=num_vertices, \n",
    "                                   radius=1, alpha=0.2, edgecolor='k')  # 创建中心在(0,0)，半径为1的正多边形\n",
    "    ax.add_patch(hexagon_inner)  # 添加多边形到坐标轴\n",
    "\n",
    "    plt.axis('off')  # 关闭坐标轴\n",
    "\n",
    "    plt.xlim(-1.5, 1.5)  # 设置x轴显示范围\n",
    "    plt.ylim(-1.5, 1.5)  # 设置y轴显示范围\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
